Symbolic manipulation for the study of the descent algebra of finite coxeter groups

AbstractIn this paper we expose how algebraic explorations with a symbolic manipulation package (Maple) led the authors (after the work of Garsia and Reutenauer, 1989) to the construction of nice basis for the descent algebras of finite Coxeter groups. This resulted in a better understanding of the multiplicative structure of many of these descent algebras. We also expose how this work was used to work out the proofs of theorems and set up the conjectures for the structure of these algebras